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  4. The area of the region enclosed between the parabolas y 2=2 x -1 and y 2=4 x -3 is

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Q. The area of the region enclosed between the parabolas $y ^{2}=2 x -1$ and $y ^{2}=4 x -3$ is

JEE MainJEE Main 2022Application of Integrals

Solution:

Required area $=2 \int\limits_{0}^{1}\left(\frac{ y ^{2}+3}{4}-\frac{ y ^{2}+1}{2}\right) dy$
$=2 \int\limits_{0}^{1} \frac{1-y^{2}}{4} d y=\frac{1}{2}\left|y-\frac{y^{3}}{3}\right|_{0}^{1}=\frac{1}{3}$

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